The Shape of The Sunspot Cycle: A One-Parameter Fit

Abstract

The empirical description of the shape of the sunspot cycle is one of the oldest problems of solar physics. Here we show that an accurate two-parameter fit is achievable where the parameters are correlated (r=0.88) for 23 solar cycles. The correlation between the parameters of our fit provides the possibility of a one-parameter fit if the times of the minima are known a priori. A one-parameter fit can also be derived from truncated dynamo models, but the goodness of the fit is not better than as achieved for the empirical fit. We suggest that the goodness of a one-parameter fit can serve as a criterion to compare different dynamo models. A one-parameter fit provides the possibility to forecast the shape of the coming cycle via a forecast of one parameter which changes synchronously with the secular variation. A previous estimation of the coming decadal average sunspot number is converted into the forecast of the shape of the 24th cycle with a maximum of 118±26 W. The accuracy is limited mostly by the uncertainties of the predicted secular variation and the uncertainty of the time of the minimum.